Finite Group Databasebeta

← #31964867

Subgroups — #31964867

Order 18176.

1070 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986533C211yesmaximal, characteristic
2C2×#17986056C211yesmaximal, characteristic, complemented
3#22586911C212yesmaximal, complemented
4#22586907C212yesmaximal
5#22586876C214yesmaximal, complemented
6#22586863C214yesmaximal, complemented
7C71×#2285C211yesmaximal, characteristic, complemented
8#17986533—21no—
9#17986533—21no—
10#17986533—21no—
11#17986533—21no—
12#17986533C412yescomplemented
13#17986533C412yescomplemented
14#17986533C2212yes—
15#17986533C2212yes—
16C2×#14556122—21no—
17C2×#14556120C411yescharacteristic, complemented
18C2×#14556116C411yescharacteristic, complemented
19C2×#14556111—21no—
20C2×#14556107C2211yescharacteristic
21C2×#14556102C2211yescharacteristic
22C2×C4×Dic142C411yescharacteristic, complemented
23C2×C4×D284C411yescharacteristic, complemented
24C2×C4×C22⋊D71—21no—
25C2×#14556085—21no—
26#17986056—21no—
27#17986056—21no—
28#17986056C2212yescomplemented
29#17986056C2212yescomplemented
30C2×C4⋊(C71⋊C8)—21no—
31C2×C22⋊(C71⋊C8)C2212yes—
32C2×#14556039—21no—
33#17985735C2218yescomplemented
34#17985732C2218yes—
35C2×#117×C71—21no—
36C22×C42×C71C2211yescharacteristic
37#384×C71—21no—
38#382×C71C2212yescomplemented
39#380×C71—21no—
40#380×C71C2212yes—
41C4×C4⋊C4×C71—21no—
42C4×C4⋊C4×C71C2212yescomplemented
43C22×Dic142C2×C411yescharacteristic
44C22×D284C2×C411yescharacteristic
45C22×C22⋊D71—21no—
46C22×C4×D71—21no—
47C22×C71⋊C8—22no—
48#14556122—22no—
49#14556122—22no—
50#14556122—22no—
51#14556122—22no—
52#14556120—21no—
53#14556120—21no—
54#14556120C2×C412yes—
55#14556120C2×C412yes—
56#14556116—21no—
57#14556116—21no—
58#14556116C2×C412yes—
59#14556116C2×C412yes—
60#14556111—22no—
61#14556111—22no—
62#14556111—22no—
63#14556111—22no—
64#14556107—21no—
65#14556107—21no—
66#14556107C2×C412yes—
67#14556107C2312yes—
68#14556102—21no—
69#14556102—21no—
70#14556102C2×C412yes—
71#14556102C2312yes—
72C4×Dic142—21no—
73C4×Dic142—21no—
74C4×Dic142C2×C412yes—
75C4×Dic142C2×C412yes—
76C4×D284—21no—
77C4×D284—21no—
78C4×D284C2×C412yes—
79C4×D284C2×C412yes—
80C4×C22⋊D71—22no—
81C4×C22⋊D71—22no—
82C4×C22⋊D71—22no—
83C4×C22⋊D71—22no—
84#14556085—22no—
85#14556085—22no—
86#14556085—22no—
87#14556085—22no—
88C2×C4⋊Dic71C2×C411yescharacteristic
89C2×C4⋊Dic71C2×C411yescharacteristic
90C2×Dic71⋊C4—21no—
91C2×Dic71⋊C4—21no—
92C2×Dic71⋊C4—21no—
93C2×Dic71⋊C4—21no—
94C2×C22⋊Dic71—21no—
95C2×(C2×D71)⋊C4—21no—
96C2×(C2×D71)⋊C4—21no—
97C2×(C2×D71)⋊C4—21no—
98C2×(C2×D71)⋊C4—21no—
99C2×C4×Dic71—21no—
100C4⋊(C71⋊C8)—22no—
101C4⋊(C71⋊C8)—22no—
102C22⋊(C71⋊C8)—22no—
103C22⋊(C71⋊C8)C2314yes—
104#14556039—22no—
105#14556039—22no—
106C23×C4×C71D411yescharacteristic
107C23×C4×C71D411yescharacteristic
108C23×C4×C71C2311yescharacteristic
109#117×C71—44no—
110C2×C4⋊C4×C71—22no—
111C2×C4⋊C4×C71—22no—
112C2×C4⋊C4×C71—22no—
113C2×C22⋊C4×C71—22no—
114C2×C42×C71—22no—
115C2×C42×C71C2×C411yescharacteristic
116C2×C42×C71C2×C411yescharacteristic
117C2×C42×C71C2×C411yescharacteristic
118C2×C42×C71C2×C411yescharacteristic
119C2×C42×C71D411yescharacteristic
120C2×C42×C71D411yescharacteristic
121C2×C42×C71D411yescharacteristic
122C2×C42×C71D411yescharacteristic
123C2×C42×C71D411yescharacteristic
124C2×C42×C71D411yescharacteristic
125C2×C42×C71C2311yescharacteristic
126C2×C42×C71C2311yescharacteristic
127#95×C71—22no—
128#95×C71C2314yes—
129C23×D71—21no—
130C2×Dic142—21no—
131C2×Dic142—42no—
132C2×Dic142C22×C412yes—
133C2×D284—21no—
134C2×D284—42no—
135C2×D284C22×C412yes—
136C2×C22⋊D71—22no—
137C2×C22⋊D71—22no—
138C2×C22⋊D71—42no—
139C2×C22⋊D71—42no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C2×C4×D71—22no—
144C2×C4×D71—22no—
145C2×C4×D71—44no—
146C2×C71⋊C8—24no—
147C2×C71⋊C8—44no—
148C4⋊Dic71—21no—
149C4⋊Dic71—21no—
150C4⋊Dic71C22×C412yes—
151C4⋊Dic71C22×C412yes—
152Dic71⋊C4—22no—
153Dic71⋊C4—22no—
154Dic71⋊C4—22no—
155Dic71⋊C4—22no—
156Dic71⋊C4—22no—
157Dic71⋊C4—22no—
158Dic71⋊C4—22no—
159Dic71⋊C4—22no—
160C22⋊Dic71—22no—
161C22⋊Dic71—22no—
162(C2×D71)⋊C4—22no—
163(C2×D71)⋊C4—22no—
164(C2×D71)⋊C4—22no—
165(C2×D71)⋊C4—22no—
166(C2×D71)⋊C4—22no—
167(C2×D71)⋊C4—22no—
168(C2×D71)⋊C4—22no—
169(C2×D71)⋊C4—22no—
170C4×Dic71—22no—
171C4×Dic71—22no—
172C24×C71C2×D411yescharacteristic
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—24no—
176C22×C4×C71—42no—
177C22×C4×C71—42no—
178C22×C4×C71C22⋊C411yescharacteristic
179C22×C4×C71C22⋊C411yescharacteristic
180C22×C4×C71C22⋊C411yescharacteristic
181C22×C4×C71C22⋊C411yescharacteristic
182C22×C4×C71C22⋊C411yescharacteristic
183C22×C4×C71C22⋊C411yescharacteristic
184C22×C4×C71C22⋊C411yescharacteristic
185C22×C4×C71C22⋊C411yescharacteristic
186C22×C4×C71C22×C411yescharacteristic
187C22×C4×C71C22×C411yescharacteristic
188C22×C4×C71C2×D411yescharacteristic
189C22×C4×C71C2×D411yescharacteristic
190C22×C4×C71C2×D411yescharacteristic
191C22×C4×C71C2×D411yescharacteristic
192C22×C4×C71C2×D411yescharacteristic
193C22×C4×C71C2×D411yescharacteristic
194C22×C4×C71C2×D411yescharacteristic
195C22×C4×C71C2411yescharacteristic
196C4⋊C4×C71—44no—
197C4⋊C4×C71—44no—
198C4⋊C4×C71—44no—
199C22⋊C4×C71—44no—
200C42×C71—44no—
201C42×C71C22⋊C411yescharacteristic
202C42×C71C22⋊C411yescharacteristic
203C42×C71C22⋊C411yescharacteristic
204C42×C71C22⋊C411yescharacteristic
205C42×C71C22⋊C411yescharacteristic
206C42×C71C22⋊C411yescharacteristic
207C42×C71C22⋊C411yescharacteristic
208C42×C71C22⋊C411yescharacteristic
209C42×C71C22×C411yescharacteristic
210C42×C71C22×C411yescharacteristic
211C42×C71C22×C411yescharacteristic
212C42×C71C22×C411yescharacteristic
213C42×C71C2×D411yescharacteristic
214C42×C71C2×D411yescharacteristic
215C42×C71C2×D411yescharacteristic
216C42×C71C2×D411yescharacteristic
217C23×C71—41no—
218C23×C71—41no—
219C23×C71C2×C22⋊C411yescharacteristic
220C23×C71C2×C22⋊C411yescharacteristic
221C23×C71AGL(1,ℤ/8)12yes—
222C23×C71#13712yes—
223C23×C71C22×D411yescharacteristic
224C22×D71—22no—
225C22×D71—42no—
226C22×D71—42no—
227C22×D71—42no—
228C2×C4×C71—21no—
229C2×C4×C71—21no—
230C2×C4×C71—21no—
231C2×C4×C71—21no—
232C2×C4×C71—22no—
233C2×C4×C71—22no—
234C2×C4×C71—22no—
235C2×C4×C71—22no—
236C2×C4×C71—22no—
237C2×C4×C71—22no—
238C2×C4×C71—22no—
239C2×C4×C71—22no—
240C2×C4×C71—22no—
241C2×C4×C71—22no—
242C2×C4×C71—41no—
243C2×C4×C71—41no—
244C2×C4×C71—41no—
245C2×C4×C71—41no—
246C2×C4×C71—41no—
247C2×C4×C71—41no—
248C2×C4×C71—44no—
249C2×C4×C71—44no—
250C2×C4×C71—44no—
251C2×C4×C71C2×C22⋊C411yescharacteristic
252C2×C4×C71C2×C22⋊C411yescharacteristic
253C2×C4×C71C2×C22⋊C411yescharacteristic
254C2×C4×C71C2×C22⋊C411yescharacteristic
255C2×C4×C71C2×C22⋊C411yescharacteristic
256C2×C4×C71C2×C22⋊C411yescharacteristic
257C2×C4×C71C2×C22⋊C411yescharacteristic
258C2×C4×C71C2×C22⋊C411yescharacteristic
259C2×C4×C71C2×C22⋊C411yescharacteristic
260C2×C4×C71C2×C22⋊C411yescharacteristic
261C2×C4×C71C23×C411yescharacteristic
262C2×C4×C71C22×D411yescharacteristic
263C22⋊D71—42no—
264C22⋊D71—42no—
265C22⋊D71—44no—
266C2×Dic71—22no—
267C2×Dic71—22no—
268C2×Dic71—22no—
269C2×Dic71—42no—
270C2×Dic71—42no—
271C2×Dic71—42no—
272D284—42no—
273D284—42no—
274C4×D71—44no—
275C4×D71—44no—
276Dic142—42no—
277Dic142—42no—
278C71⋊C8—44no—
279C22×C71—21no—
280C22×C71—21no—
281C22×C71—21no—
282C22×C71—21no—
283C22×C71—21no—
284C22×C71—21no—
285C22×C71—42no—
286C22×C71—42no—
287C22×C71#41712yes—
288C22×C71#41712yes—
289C22×C71C22×C22⋊C411yescharacteristic
290C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C71C2×#13711yescharacteristic
292C2×D71—42no—
293C2×D71—42no—
294C2×D71—42no—
295C2×D71—84no—
296C4×C71—21no—
297C4×C71—21no—
298C4×C71—21no—
299C4×C71—21no—
300C4×C71—21no—
301C4×C71—21no—
302C4×C71—21no—
303C4×C71—21no—
304C4×C71—21no—
305C4×C71—21no—
306C4×C71—84no—
307C4×C71#41012yes—
308C4×C71#42112yes—
309Dic71—42no—
310Dic71—42no—
311Dic71—42no—
312#17581—711nomaximal, Sylow
313C2×C71—21no—
314C2×C71—22no—
315C2×C71—21no—
316C2×C71—22no—
317C2×C71C2×#41011yescharacteristic
318C2×C71C2×#41711yescharacteristic
319C2×C71C2×#42111yescharacteristic
320D71—82no—
321C2×#529—711no—
322C2×#432—711no—
323#2285D7111yescharacteristic, complemented
324#1520—712no—
325#1519—712no—
326#1512—714no—
327#1509—714no—
328C71#1758111yescharacteristic, complemented, Sylow
329#529—712no—
330#529—712no—
331#529—712no—
332#529—712no—
333#529—1421no—
334#529—1421no—
335#529—1421no—
336#529—1421no—
337C2×#126—1421no—
338C2×#125—711no—
339C2×#124—711no—
340C2×#123—1421no—
341C2×C22⋊Q8—711no—
342C2×#121—711no—
343C2×C4×Q8—711no—
344C2×C4×D4—711no—
345C2×C4×D4—1421no—
346C2×#117—21no—
347C2×#117—1421no—
348C22×C42C2×D7111yescharacteristic
349#432—712no—
350#432—712no—
351#432—1421no—
352#432—1421no—
353C2×C4⋊C8—1421no—
354C2×C22⋊C8—712no—
355C2×#97—1421no—
356#384—21no—
357#382C2×D7112yescomplemented
358#380—21no—
359#380C2×D7112yes—
360C4×C4⋊C4—21no—
361C4×C4⋊C4C2×D7112yescomplemented
362#328—718no—
363#327—718no—
364C22×Q8—711no—
365C22×D4—711no—
366C22×D4—1421no—
367C23×C4—1421no—
368C23×C4C22⋊D7111yescharacteristic
369C23×C4C22⋊D7111yescharacteristic
370C23×C4C22×D7111yescharacteristic
371C22×C8—1422no—
372#126—1422no—
373#126—1422no—
374#126—1422no—
375#126—1422no—
376#125—712no—
377#125—712no—
378#125—1421no—
379#125—1421no—
380#124—712no—
381#124—712no—
382#124—1421no—
383#124—1421no—
384#123—1422no—
385#123—1422no—
386#123—1422no—
387#123—1422no—
388C22⋊Q8—712no—
389C22⋊Q8—712no—
390C22⋊Q8—1421no—
391C22⋊Q8—1421no—
392#121—712no—
393#121—712no—
394#121—1421no—
395#121—1421no—
396C4×Q8—712no—
397C4×Q8—712no—
398C4×Q8—1421no—
399C4×Q8—1421no—
400C4×D4—712no—
401C4×D4—712no—
402C4×D4—1422no—
403C4×D4—1422no—
404C4×D4—1422no—
405C4×D4—1422no—
406C4×D4—1421no—
407C4×D4—1421no—
408#117—44no—
409#117—1422no—
410#117—1422no—
411#117—1422no—
412#117—1422no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—711no—
417C2×C4⋊C4—711no—
418C2×C4⋊C4—1421no—
419C2×C4⋊C4—1421no—
420C2×C4⋊C4—1421no—
421C2×C4⋊C4—1421no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—1421no—
424C2×C22⋊C4—1421no—
425C2×C22⋊C4—1421no—
426C2×C22⋊C4—1421no—
427C2×C22⋊C4—1421no—
428C2×C42—22no—
429C2×C42—1421no—
430C2×C42C4×D7111yescharacteristic
431C2×C42C4×D7111yescharacteristic
432C2×C42C4×D7111yescharacteristic
433C2×C42C4×D7111yescharacteristic
434C2×C42D28411yescharacteristic
435C2×C42D28411yescharacteristic
436C2×C42D28411yescharacteristic
437C2×C42D28411yescharacteristic
438C2×C42C22⋊D7111yescharacteristic
439C2×C42C22⋊D7111yescharacteristic
440C2×C42C22×D7111yescharacteristic
441C2×C42C22×D7111yescharacteristic
442C4⋊C8—1422no—
443C4⋊C8—1422no—
444C22⋊C8—714no—
445C22⋊C8—1422no—
446#97—1422no—
447#97—1422no—
448#95—22no—
449#95C22×D7114yes—
450C24—1421no—
451C24C2×C22⋊D7111yescharacteristic
452C2×Q8—2842no—
453C2×Q8—712no—
454C2×Q8—1421no—
455C2×D4—2842no—
456C2×D4—2842no—
457C2×D4—2842no—
458C2×D4—712no—
459C2×D4—1422no—
460C2×D4—1422no—
461C2×D4—1421no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—2844no—
468C22×C4—1421no—
469C22×C4—1421no—
470C22×C4—1421no—
471C22×C4—1422no—
472C22×C4—1422no—
473C22×C4(C2×D71)⋊C411yescharacteristic
474C22×C4(C2×D71)⋊C411yescharacteristic
475C22×C4(C2×D71)⋊C411yescharacteristic
476C22×C4(C2×D71)⋊C411yescharacteristic
477C22×C4(C2×D71)⋊C411yescharacteristic
478C22×C4(C2×D71)⋊C411yescharacteristic
479C22×C4(C2×D71)⋊C411yescharacteristic
480C22×C4(C2×D71)⋊C411yescharacteristic
481C22×C4C2×C4×D7111yescharacteristic
482C22×C4C2×C4×D7111yescharacteristic
483C22×C4C2×C22⋊D7111yescharacteristic
484C22×C4C2×C22⋊D7111yescharacteristic
485C22×C4C2×C22⋊D7111yescharacteristic
486C22×C4C2×C22⋊D7111yescharacteristic
487C22×C4C2×C22⋊D7111yescharacteristic
488C22×C4C2×D28411yescharacteristic
489C22×C4C2×D28411yescharacteristic
490C22×C4C23×D7111yescharacteristic
491C2×C8—2844no—
492C2×C8—1424no—
493C4⋊C4—44no—
494C4⋊C4—44no—
495C4⋊C4—44no—
496C4⋊C4—712no—
497C4⋊C4—712no—
498C4⋊C4—1422no—
499C4⋊C4—1422no—
500C4⋊C4—1422no—
501C4⋊C4—1422no—
502C4⋊C4—1422no—
503C4⋊C4—1422no—
504C4⋊C4—1422no—
505C4⋊C4—1422no—
506C4⋊C4—1421no—
507C4⋊C4—1421no—
508C22⋊C4—44no—
509C22⋊C4—1422no—
510C22⋊C4—1422no—
511C22⋊C4—1422no—
512C22⋊C4—1422no—
513C22⋊C4—1422no—
514C22⋊C4—1422no—
515C22⋊C4—1422no—
516C22⋊C4—1422no—
517C22⋊C4—1422no—
518C22⋊C4—1422no—
519C42—44no—
520C42—1422no—
521C42—1422no—
522C42(C2×D71)⋊C411yescharacteristic
523C42(C2×D71)⋊C411yescharacteristic
524C42(C2×D71)⋊C411yescharacteristic
525C42(C2×D71)⋊C411yescharacteristic
526C42(C2×D71)⋊C411yescharacteristic
527C42(C2×D71)⋊C411yescharacteristic
528C42(C2×D71)⋊C411yescharacteristic
529C42(C2×D71)⋊C411yescharacteristic
530C42C2×C4×D7111yescharacteristic
531C42C2×C4×D7111yescharacteristic
532C42C2×C4×D7111yescharacteristic
533C42C2×C4×D7111yescharacteristic
534C42C2×D28411yescharacteristic
535C42C2×D28411yescharacteristic
536C42C2×D28411yescharacteristic
537C42C2×D28411yescharacteristic
538C23—41no—
539C23—41no—
540C23—2842no—
541C23—2842no—
542C23—2842no—
543C23—1422no—
544C23C2×(C2×D71)⋊C411yescharacteristic
545C23C2×(C2×D71)⋊C411yescharacteristic
546C23#1455615412yes—
547C23#1455615912yes—
548C23C22×C22⋊D7111yescharacteristic
549Q8—2842no—
550Q8—2842no—
551D4—2842no—
552D4—2844no—
553D4—2842no—
554D4—2842no—
555D4—2842no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—2844no—
580C2×C4—2842no—
581C2×C4—2842no—
582C2×C4—2842no—
583C2×C4—2844no—
584C2×C4—1422no—
585C2×C4—1422no—
586C2×C4—1422no—
587C2×C4C2×(C2×D71)⋊C411yescharacteristic
588C2×C4C2×(C2×D71)⋊C411yescharacteristic
589C2×C4C2×(C2×D71)⋊C411yescharacteristic
590C2×C4C2×(C2×D71)⋊C411yescharacteristic
591C2×C4C2×(C2×D71)⋊C411yescharacteristic
592C2×C4C2×(C2×D71)⋊C411yescharacteristic
593C2×C4C2×(C2×D71)⋊C411yescharacteristic
594C2×C4C2×(C2×D71)⋊C411yescharacteristic
595C2×C4C2×(C2×D71)⋊C411yescharacteristic
596C2×C4C2×(C2×D71)⋊C411yescharacteristic
597C2×C4C22×C4×D7111yescharacteristic
598C2×C4C22×D28411yescharacteristic
599C8—2844no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—42no—
607C22—42no—
608C22—2842no—
609C22—2842no—
610C22—2842no—
611C22—5684no—
612C22#1798599812yes—
613C22#1798599812yes—
614C22C22×(C2×D71)⋊C411yescharacteristic
615C22C2×#1455615411yescharacteristic
616C22C2×#1455615911yescharacteristic
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—84no—
628C4—2842no—
629C4—2842no—
630C4—2842no—
631C4#1798597212yes—
632C4#1798601712yes—
633C2—21no—
634C2—22no—
635C2—22no—
636C2—21no—
637C2—5682no—
638C2C2×#1798597211yescharacteristic
639C2C2×#1798599811yescharacteristic
640C2C2×#1798601711yescharacteristic
subgroupG/H
centerC22C22×(C2×D71)⋊C4
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2285C2
socleC22×C71C22×C22⋊C4
prime radicalC2×#14556102C22
cosocleC22×C4×C71C24
hypercenter#2285D71
hypocenterC71#17581
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2285

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#17986056C2semidirect
3. #22586911C2semidirect
5. #22586876C2semidirect
6. #22586863C2semidirect
7. C71×#2285C2semidirect
12. #17986533C4semidirect
13. #17986533C4semidirect
17. C2×#14556120C4semidirect
18. C2×#14556116C4semidirect
22. C2×C4×Dic142C4semidirect
23. C2×C4×D284C4semidirect
28. #17986056C22semidirect
29. #17986056C22semidirect
33. #17985735C22semidirect
38. #382×C71C22semidirect
42. C4×C4⋊C4×C71C22semidirect
323. #2285D71semidirect
328. C71#17581semidirect
357. #382C2×D71semidirect
361. C4×C4⋊C4C2×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179865332
C2×#179860562
#225869112
#225869072
#225868762
#225868632
C71×#22852
#1758171